Well logging tools are commonly used in well drilling and production operations to characterise wells. Such tools may comprise e.g. gamma-ray or electrical resistivity sensors which provide information on the lithology of the rock formation traversed by the well. Most sensors are set up to make measurements at regular time intervals as the logging tool travels along the well. Thus typically a log produced by a sensor comprises a series of measurements taken at particular times which correspond to spaced positions along the well. However, a problem arises when the logging tool velocity varies, as the longitudinal spacing of the measurement positions also then varies and the resulting log can be difficult to interpret.
Furthermore, when different logs are produced for the same stretch of well by a logging tool having spaced sensors or by the same sensor at different times, it can be difficult properly to match or correlate the features of one log with the features of another because of the variation in measurement position.
This problem is particularly acute for LWD (Logging While Drilling) operations because the process of drilling generally involves irregular drill string movements and hence large changes in velocity (and even reversals of direction) of the logging tool. Thus LWD logging tool velocity is prone to significantly more variation than the velocity of e.g. a logging tool or “sonde” controlled by a wireline.
During well drilling it is usually important to be able to determine the position and/or rate of penetration of the drill bit. However, while the movement of a drill bit is controlled to a significant extent by the movement of the drill string at the well surface which in turn is controlled by the hook load applied to the drill string, the precise way in which these parameters impact on the movement of the drill bit can be complicated. This is because the apparent compliance of the drill string is not determined solely by the physical properties and length of the drill string. Thus a correction needs to be introduced if the surface movement of the drill string is to be used to predict the downhole movement of the drill bit.
The apparent compliance of the drill string can be influenced by many factors. For example, there is usually significant friction between the string and the walls of the well, as well as changing thrust loads exerted on the string. Insofar as these factors can be determined with any precision, they add considerable complexity to the determination of the drill string compliance. Inaccuracies, such as calibration problems, wear etc., in the surface draw works system for measuring block height may also be complicating factors. Thus mere knowledge of the instantaneous hook load and the instantaneous velocity of the drill string at the surface may not supply the well operator with enough information to correct the relative depth and penetration rate of the drill bit with sufficient accuracy.
In an attempt to overcome this problem, U.S. Pat. No. 4,843,875 describes a procedure for measuring drill bit rate of penetration which assumes that the behaviour of the drill string can be modelled by a relationship of the form:
      V    F    =            V      S        +          λ      ⁢                        ⅆ          F                          ⅆ          t                    where VF is the instantaneous velocity of the drill bit, VS is the instantaneous velocity of the drill string at the surface, λ is the apparent compliance of the drill string, and dF/dt is the first derivative with respect to time of the weight F suspended from the hook.
To be fully effective this approach requires a very good hookload measurement—so that not only the hookload but also the rate-of-change of hookload can be accurately derived. Errors due to friction in the rig apparatus can produce significant errors in the rate-of-change of hookload.
An alternative procedure, described in U.S. Pat. No. 5,321,982, uses a well tool having at least two logging sensors which are spaced a known distance apart in the direction of movement of the tool. By matching the logs produced by the sensors it is possible to determine the instantaneous velocity (i.e. rate of penetration) of the tool. However, because drill bit penetration rates generally do not vary smoothly, this approach has little predictive capacity for drilling operations.
U.S. Pat. No. 5,522,260 discloses a procedure for performing depth correction on a logging tool having two spaced sensors in which the tool is provided with an accelerometer. In this procedure, the tool velocity determined by correlating the sensor logs is combined with the tool velocity determined by the accelerometer to produce a depth correction for the tool. However, this procedure is not particularly suitable for LWD operations because LWD logging tools are not usually provided with accelerometers.